Question 198271


Start with the given system of equations:



{{{system(x+y=7,x-y=1)}}}



In order to graph these equations, we <font size="4"><b>must</b></font> solve for y first.



Let's graph the first equation:



{{{x+y=7}}} Start with the first equation.



{{{y=7-x}}} Subtract {{{x}}} from both sides.



{{{y=-x+7}}} Rearrange the terms and simplify.



Now let's graph the equation:



{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,-x+7)
)}}} Graph of {{{y=-x+7}}}.



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Now let's graph the second equation:



{{{x-y=1}}} Start with the second equation.



{{{-y=1-x}}} Subtract {{{x}}} from both sides.



{{{y=(1-x)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}.



{{{y=x-1}}} Rearrange the terms and simplify.



Now let's graph the equation:



{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,x-1)
)}}} Graph of {{{y=x-1}}}.



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Now let's graph the two equations together:



{{{drawing(500,500,-10,10,-10,10,
grid(1),
graph(500,500,-10,10,-10,10,-x+7,x-1)
)}}} Graph of {{{y=-x+7}}} (red). Graph of {{{y=x-1}}} (green)



From the graph, we can see that the two lines intersect at the point *[Tex \LARGE \left(4,3\right)]. So the solution to the system of equations is *[Tex \LARGE \left(4,3\right)]. This tells us that the system of equations is consistent and independent.